What are the strategic actions to sell the largest quantity of products at prices that produce a greater total margin ?

There are only two ways to increase your margin:  decrease costs or increase prices.  The problem is that successfully increasing prices usually involves a cost, and decreasing costs usually means you have to cut prices eventually (perhaps because product quality, customer service or marketing is reduced).

The key action in increasing your margin is to be very clear about what strategy you will use to achieve it.   Lower costs or higher prices? 

(Of course you should always be looking to keep costs under control and prices as high as possible, your question refers to the particular circumstance of a strategic initiative.)

I would add two points.  Firstly, the relationship with the customer is crucial.  If you have a great relationship with your customers, everything else is much easier.

The second is that price doesn't matter.   Let's take a price as an example, let's say $.  Is that a good price? 

But, you will reply, I can't tell if it's a good price until you say what the product is.   Exactly!   $ is a brilliant price for a new Aston Martin, but rubbish value for a pint of milk.  It's not price that matters, it's value.